Secondly, methodology has its source in the methods themselves which actually, and therefore technically, develop in the various fields of our knowledge out of the problems peculiar to those fields.
It is the office of scientific thought to interpret validly the objects that are presented to us in outer and inner perception, and that can be derived from both these sources. We accomplish this interpretation entirely through judgments and combinations of judgments of manifold sorts. The concepts, which the older logic regarded as the true elementary forms of our thinking, are only certain selected types of judgment, such stereotyped judgments as those which make up definitions and cla.s.sifications, and which appear independent and fundamental because their subject-matter, that is, their intension or extension, is connected through the act of naming with certain words. Scientific methods, then, are the ways and means by which our thought can accomplish and set forth, in accordance with its ideal, this universally valid interpretation.
There belongs, accordingly, to methodology a list of problems which we can divide, to be sure only _in abstracto_, into three separate groups.
First, methodology has to a.n.a.lyze the methods which have been technically developed in the different fields of knowledge into the elementary forms of our thinking from which they have been built up.
Next to this work of _a.n.a.lyzing_, there comes a second task which may be called a _normative_ one; for it follows that we must set forth and deduce systematically from their sources the nature of these manifold elements, their resulting connection, and their validity. To these two offices must be added a third that we may call _a potiori_ a _synthetic_ one; for finally we must reconstruct out of the elements of our thinking, as revealed by a.n.a.lysis, the methods belonging to the different fields of knowledge and also determine their different scope and validity.
The beginning of another conception of the office of methodology can be found in those thoughts which have become significant, especially in Leibnitz"s fragments and drafts of a _calculus ratiocinator_ or a _specieuse generale_. The foregoing discussion has set aside all hope that these beginnings and their recent development may give, of the possibility of constructing the manifold possible methods _a priori_, that is, before or independent of experience. However, it remains entirely undecided, as it should in this our preliminary account of the office of general methodology, whether or not all methods of our scientific thought will prove to be ultimately but branches of one and the same universal method, a thought contained in the undertakings just referred to. Although modern empiricism, affiliated as it is with natural science, tends to answer this question in the affirmative even more definitely and dogmatically than any type of the older rationalism, still the question is one that can be decided only in the course of methodological research.
The conception of a methodology of scientific thought can be said to be almost as old as scientific thought itself; for it is already contained essentially, though undifferentiated, in the Socratic challenge of knowledge. None the less, the history of methodology, as the history of every other science, went through the course of which Kant has given a cla.s.sical description. "No one attempts to construct a science unless he can base it on some idea; but in the elaboration of it the schema, nay, even the definition which he gives in the beginning of his science, corresponds very seldom to his idea, which, like a germ, lies hidden in the reason, and all the parts of which are still enveloped and hardly distinguishable even under microscopical observation."[5]
[Footnote 5: Kant, _Kr. d. r. V._, 2d ed., p. 862.]
We are indebted to the Greek, and especially to the Platonic-Aristotelian philosophy for important contributions to the understanding of the deductive method of mathematical thought. It was precisely this trend of philosophic endeavor which, though furnishing for the most part the foundation of methodological doctrine well on into the seventeenth century, offered no means of differentiating the methods that are authoritative for our knowledge of facts. What Socrates was perhaps the first to call "induction," is essentially different, as regards its source and aim, from the inductive methods that direct our research in natural and mental science. For it is into these two fields that we have to divide the totality of the sciences of facts, the material sciences, let us call them, in opposition to the formal or mathematical sciences,--that is, if we are to do justice to the difference between sense and self perception, or "outer" and "inner"
perception.
Two closely connected forces especially led astray the methodological opinions regarding the material sciences till the end of the eighteenth century, and in part until the beginning of the nineteenth century. We refer, in the first place, to that direction of thought which gives us the right to characterize the Platonic-Aristotelian philosophy as a "concept philosophy;" namely, the circ.u.mstance that Aristotelian logic caused the "concept" to be set before the "judgment." In short, we refer to that tendency in thought which directs the attention not to the permanent in the world"s occurrences, the uniform connections of events, but rather to the seemingly permanent in the things, their essential attributes or essences. Thus the concept philosophy, as a result of its tendency to hypostasize, finds in the abstract general concepts of things, the ideas, the eternal absolute reality that const.i.tutes the foundation of things and is contained in them beside the accidental and changing properties.[6] Here we have at once the second force which inspired the ancient methodology. These ideas, like the fundamentally real, const.i.tute that which ultimately alone acts in all the coming into existence and the going out of existence of the manifold things. In the Aristotelian theory of causation, this thought is made a principle; and we formulate only what is contained in it, when we say that, according to it, the efficient and at the same time final causes can be deduced through mere a.n.a.lysis from the essential content of the effects; that, in fact, the possible effects of every cause can be deduced from the content of its definition. The conceptual determination of the causal relation, and with it in principle the sum total of the methods in the material sciences, becomes a logical, a.n.a.lytical, and deductive one.
These sciences remain entirely independent of the particular content of experience as this broadens, and so do also the methods under discussion.
[Footnote 6: According to Plato, it is true, the ideas are separated from the sensible things; they must be thought in a conceptual place, for the s.p.a.ce of sense perception is to be understood as non-being, matter. The things revealed to sense, however, occupy a middle position between being and non-being, so that they partake of the ideas. In this sense, the statement made above holds also of the older view of the concept philosophy.]
As a consequence, every essential difference between mathematical thought and the science of causes is done away with in favor of a rationalistic construction of the methods of material science.
Accordingly, throughout the seventeenth century, the ideal of all scientific method becomes, not the inductive method that founded the new epoch of the science of to-day, but the deductive mathematical method applied to natural scientific research. The flourish of trumpets with which Francis Bacon hailed the onslaught of the inductive methods in the natural science of the time, helped in no way; for he failed to remodel the traditional, Aristotelian-Scholastic conception of cause, and, accordingly, failed to understand both the problem of induction and the meaning of the inductive methods of the day.[7] Descartes, Hobbes, Spinoza, and related thinkers develop their _mathesis universalis_ after the pattern of geometrical thinking. Leibnitz tries to adapt his _specieuse generale_ to the thought of mathematical a.n.a.lysis. The old methodological conviction gains its clear-cut expression in Spinoza"s doctrine: "_Aliquid efficitur ab aliqua re_" means "_aliquid sequitur ex ejus definitione_."
[Footnote 7: Cf. the articles on Francis Bacon by Chr.
Sigwart in the _Preussische Jahrbucher_, xii, 1863, and xiii, 1864.]
The logically straight path is seldom the one taken in the course of the history of thought. The new formulation and solution of problems influence us first through their evident significance and consequences, not through the traditional presuppositions upon which they are founded.
Thus, in the middle of the seventeenth century, when insight into the precise difference between mental and physical events gave rise to pressing need for its definite formulation, no question arose concerning the dogmatic presupposition of a purely logical (_a.n.a.lytisch_) relationship between cause and effect; but, on the contrary, this presupposition was then for the first time brought clearly before consciousness. It was necessary to take the roundabout way through occasionalism and the preestablished harmony, including the latter"s retreat to the omnipotence of G.o.d, before it was possible to miss the question of the validity of the presupposition that the connection between cause and effect is a.n.a.lytic and rational.
Among the leading thinkers of the period this problem was recognized as the cardinal problem of contemporaneous philosophy. It is further evidence how thoroughly established this problem must have been among the more deeply conceived problems of the time in the middle of the eighteenth century, that Hume and Kant were forced to face it, led on, seemingly independently of each other, and surely from quite different presuppositions and along entirely different ways. The historical evolution of that which from the beginning has seemed to philosophy the solving of her true problem has come to pa.s.s in a way not essentially different from that of the historical evolution in all other departments of human knowledge. Thus, in the last third of the seventeenth century, Newton and Leibnitz succeeded in setting forth the elements of the infinitesimal calculus; and, in the fifth decade of the nineteenth century, Robert Mayer, Helmholtz, and perhaps Joule, formulated the law of the conservation of energy. In one essential respect Hume and Kant are agreed in the solution of the new, and hence contemporaneously misunderstood, problem. Both realized that the connection between the various causes and effects is not a rational a.n.a.lytic, but an empirical synthetic one. However, the difference in their presuppositions as well as method caused this common result to make its appearance in very different light and surroundings. In Hume"s empiricism the connection between cause and effect appears as the mere empirical result of a.s.sociation; whereas in Kant"s rationalism this general relation between cause and effect becomes the fundamental condition of all possible experience, and is, as a consequence, independent of all experience. It rests, as a means of connecting our ideas, upon an inborn uniformity of our thought.
Thus the way was opened for a fundamental separation of the inductive material scientific from the deductive mathematical method. For Hume mathematics becomes the science of the relations of ideas, as opposed to the sciences of facts. For Kant philosophical knowledge is the knowledge of the reason arising from concepts, whereas the mathematical is that arising from the construction of concepts. The former, therefore, studies the particular only in the universal; the latter, the universal in the particular, nay, rather in the individual.
Both solutions of the new problem which in the eighteenth century supplant the old and seemingly self-evident presupposition, appear accordingly embedded in the opposition between the rationalistic and empiristic interpretation of the origin and validity of our knowledge, the same opposition that from antiquity runs through the historical development of philosophy in ever new digressions.
Even to-day the question regarding the meaning and the validity of the causal connection stands between these contrary directions of epistemological research; and the ways leading to its answer separate more sharply than ever before. It is therefore more pressing in our day than it was in earlier times to find a basis upon which we may build further epistemologically and therefore methodologically. The purpose of the present paper is to seek such a basis for the different methods employed in the sciences of facts.
As has already been said, the contents of our consciousness, which are given us immediately in outer and inner perception, const.i.tute the raw material of the sciences of facts. From these various facts of perception we derive the judgments through which we predict, guide, and shape our future perception in the course of possible experience. These judgments exist in the form of reproductive ideational processes, which, if logically explicit, become _inductive inferences_ in the broader sense. These inferences may be said to be of two sorts, though fundamentally only two sides of one and the same process of thought; they are in part a.n.a.logical inferences and in part _inductive inferences in the narrower sense_. The former infers from the particular in a present perception, _which in previous perceptions was uniformly connected with other particular contents of perception_, to a particular that resembles _those other contents of perception_. In short, they are inferences from a particular to a particular. After the manner of such inferences we logically formulate, for example, the reproductive processes, whose conclusions run: "This man whom I see before me, is attentive, feels pain, will die;" "this meteor will prove to have a chemical composition similar to known meteors, and also to have corresponding changes on its surface as the result of its rapid pa.s.sage through our atmosphere." The inductive inferences in the narrower sense argue, on the contrary, from the perceptions of a series of uniform phenomena to a universal, which includes the given and likewise all possible cases, in which a member of the particular content of the earlier perceptions is presupposed as given. In short, they are conclusions from a particular to a universal that is more extensive than the sum of the given particulars. For example: "All men have minds, will die;" "all meteoric stones will prove to have this chemical composition and those changes of surface."
There is no controversy regarding the inner similarity of both these types of inference or regarding their outward structure; or, again, regarding their outward difference from the deductive inferences, which proceed not from a particular to a particular or general, but from a general to a particular.
There is, however, difference of opinion regarding their inner structure and their inner relation to the deductive inferences. Both questions depend upon the decision regarding the meaning and validity of the causal relation. The contending parties are recruited essentially from the positions of traditional empiricism and rationalism and from their modern offshoots.
We maintain first of all:
1. The _presupposition_ of all inductive inferences, from now on to be taken in their more general sense, is, that the contents of perception are given to us _uniformly_ in repeated perceptions, that is, in uniform components and uniform relations.
2. The _condition_ of the validity of the inductive inferences lies in the thoughts that _the same causes will be present_ in the un.o.bserved realities as in the observed ones, and that _these same causes will bring forth the same effects_.
3. The _conclusions_ of all inductive inferences have, logically speaking, purely _problematic_ validity, that is, their contradictory opposite remains equally thinkable. They are, accurately expressed, merely _hypotheses_, whose validity needs verification through future experience.
The first-mentioned _presupposition_ of inductive inference must not be misunderstood. The paradox that nothing really repeats itself, that each stage in nature"s process comes but once, is just as much and just as little justified as the a.s.sertion, everything has already existed. It does not deny the fact that we can discriminate in the contents of our perceptions the uniformities of their components and relations, in short, that similar elements are present in these ever new complexes.
This fact makes it possible that our manifold perceptions combine to make up one continuous experience. Even our paradox presupposes that the different contents of our perceptions are comparable with one another, and reveal accordingly some sort of common nature. All this is not only a matter of course for empiricism, which founds the whole const.i.tution of our knowledge upon habits, but must also be granted by every rationalistic interpretation of the structure of knowledge. Every one that is well informed knows that what we ordinarily refer to as facts already includes a theory regarding them. Kant judges in this matter precisely as Hume did before him and Stuart Mill after him. "If cinnabar were sometimes red and sometimes black, sometimes light and sometimes heavy, if a man could be changed now into this, now into another animal shape, if on the longest day the fields were sometimes covered with fruit, sometimes with ice and snow, the faculty of my empirical imagination would never be in a position, when representing red color, to think of heavy cinnabar."[8]
[Footnote 8: Kant, _Kr. d. r. V._, 1st ed., pp. 100 f.]
The a.s.sumption that in recurring perceptions similar elements of content, as well as of relation, are given, is a necessary condition of the possibility of experience itself, and accordingly of all those processes of thought which lead us, under the guidance of previous perceptions, from the contents of one given perception to the contents of possible perceptions.
A tradition from Hume down has accustomed us to a.s.sociate the relation of cause and effect not so much with the uniformity of coexistence as with the uniformity of sequence. Let us for the present keep to this tradition. Its first corollary is that the relation of cause and effect is to be sought in the uninterrupted flow and connection of events and changes. The cause becomes the uniformly preceding event, the constant _antecedens_, the effect the uniformly following, the constant _consequens_, in the course of the changes that are presented to consciousness as a result of foregoing changes in our sensorium.
According to this tradition that we have taken as our point of departure, the uniformity of the sequence of events is a necessary presupposition of the relation between cause and effect. This uniformity is given us as an element of our experience; for we actually find uniform successions in the course of the changing contents of perception. Further, as all our perceptions are in the first instance sense perceptions, we may call them the sensory presupposition of the possibility of the causal relation.
In this presupposition, however, there is much more involved than the name just chosen would indicate. The uniformity of sequence lies, as we saw, not in the contents of perception as such, which are immediately given to us. It arises rather through the fact that, in the course of repeated perceptions, we apprehend through abstraction the uniformities of their temporal relation. Moreover, there lie in the repeated perceptions not only uniformities of sequence, but also uniformities of the qualitative content of the successive events themselves, and these uniformities also must be apprehended through abstraction. Thus these uniform contents of perception make up series of the following form:
_a_1 --> _b_1 _a_2 --> _b_2 " "
_a_n --> _b_n
The presupposition of the possibility of the causal relations includes, therefore, more than mere perceptive elements. It involves the relation of different, if you will, of peculiar contents of perception, by virtue of which we recognize _a_2 --> _b_2 ... _a_n --> _b_n as events that resemble one another and the event _a_1 --> _b_1 qualitatively as well as in their sequence. There are accordingly involved in our presupposition _reproductive_ elements which indicate the action of memory. In order that I may in the act of perceiving _a_3 --> _b_3 apprehend the uniformity of this present content with that of _a_2 --> _b_2 and _a_1 --> _b_1, these earlier perceptions must in some way, perhaps through memory,[9] be revived with the present perception.
[Footnote 9: It is not our present concern to ascertain how this actually happens. The psychological presuppositions of the present paper are contained in the theory of reproduction that I have worked out in connection with the psychology of speech in the articles on "Die psychologischen Grundlagen der Beziehungen zwischen Sprechen und Denken,"
_Archiv fur systematische Philosophie_, II, III, und VII; cf. note 1, page 151.]
In this reproduction there is still a further element, which can be separated, to be sure only _in abstracto_, from the one just pointed out. The present revived content, even if it is given in memory as an independent mental state, is essentially different from the original perception. It differs in all the modifications in which the memory of lightning and thunder could differ from the perception of their successive occurrence, or, again, the memory of a pain and the resulting disturbance of attention could differ from the corresponding original experience. However, as memory, the revived experience presents itself as a picture of that which has been previously perceived. Especially is this the case in memory properly so called, where the peculiar s.p.a.ce and time relations individualize the revived experience. If we give to this identifying element in the a.s.sociative process a logical expression, we shall have to say that there is involved in revival, and especially in memory, an awareness that the present ideas recall the same content that was previously given us in perception. To be sure, the revival of the content of previous perceptions does not have to produce ideas, let alone memories. Rapid, transitory, or habitual revivals, stimulated by a.s.sociative processes, can remain unconscious, that is, they need not appear as ideas or states of consciousness. Stimulation takes place, but consciousness does not arise, provided we mean by the term "consciousness" the genus of our thoughts, feelings, and volitions. None the less it must not be forgotten that this awareness of the essential ident.i.ty of the present revived content with that of the previous perception can be brought about in every such case of reproduction. How all this takes place is not our present problem.
We can apply to this second element in the reproductive process, which we have found to be essential to the causal relation, a Kantian term, "Recognition." This term, however, is to be taken only in the sense called for by the foregoing statements; for the rationalistic presuppositions and consequences which mark Kant"s "Synthesis of Recognition" are far removed from the present line of thought.
We may, then, sum up our results as follows: In the presupposition of a uniform sequence of events, which we have accepted from tradition as the necessary condition of the possibility of the causal relation, there lies the thought that the contents of perception given us through repeated sense stimulation are related to one another through a reproductive recognition.
The a.s.sumption of such reproductive recognition is not justified merely in the cases so far considered. It is already necessary in the course of the individual perceptions _a_ and _b_, and hence in the apprehension of an occurrence. It makes the sequence itself in which _a_ and _b_ are joined possible; for in order to apprehend _b_ as following upon _a_, in case the perception of _a_ has not persisted in its original form, _a_ must be as far revived and recognized upon _b_"s entrance into the field of perception as it has itself pa.s.sed out of that field. Otherwise, instead of _b_ following upon _a_ and being related to _a_, there would be only the relationless change from _a_ to _b_. This holds generally and not merely in the cases where the perception of _a_ has disappeared before that of _b_ begins, for example, in the case of lightning and thunder, or where it has in part disappeared, for example, in the throwing of a stone.
We have represented _a_ as an event or change, in order that uniform sequences of events may alone come into consideration as the presupposition of the causal relation. But every event has its course in time, and is accordingly divisible into many, ultimately into infinitely many, shorter events. Now if _b_ comes only an infinitely short interval later than _a_, and by hypothesis it must come later than _a_, then a corresponding part of _a_ must have disappeared by the time _b_ appears.
But the infinitesimal part of a perception is just as much out of all consideration as would be an infinitely long perception; all which only goes to show that we have to subst.i.tute intervals of finite length in place of this purely conceptual a.n.a.lysis of a continuous time interval.
This leaves the foregoing discussion as it stands. If _b_ follows _a_ after a perceptible finite interval, then the flow or development of _a_ by the time of _b_"s appearance must have covered a course corresponding to that interval; and all this is true even though the earlier stages of _a_ remain unchanged throughout the interval preceding _b_"s appearance.
The present instant of flow is distinct from the one that has pa.s.sed, even though it takes place in precisely the same way. The former, not the latter, gives the basis of relation which is here required, and therefore the former must be reproduced and recognized. This thought also is included in the foregoing summary of what critical a.n.a.lysis shows to be involved in the presupposition of a uniform sequence.
In all this we have already abandoned the field of mere perception which gave us the point of departure for our a.n.a.lysis of uniform sequence. We may call the changing course of perception only in the narrower meaning the sensory presupposition of the causal relation. In order that these changing contents of perception may be known as like one another, as following one another, and as following one another uniformly, they must be related to one another through a recognitive reproduction.
Our critical a.n.a.lysis of uniform sequence is, however, not yet complete.
To relate to one another the contents of two ideas always requires a process at once of identifying and of differentiating, which makes these contents members of the relation, and which accordingly presupposes that our attention has been directed to each of the two members as well as to the relation itself--in the present case, to the sequence. Here we come to another essential point. We should apply the name "thought" to every ideational process in which attention is directed to the elements of the mental content and which leads us to identify with one another, or to differentiate from one another, the members of this content.[10] The act of relating, which knows two events as similar, as following one another, indeed, as following one another uniformly, is therefore so far from being a sensation that it must be claimed to be an act of thinking.
The uniformity of sequence of _a_ and _b_ is therefore an act of relating on the part of our thought, so far as this becomes possible solely through the fact that we at one and the same time identify with one another and differentiate from one another _a_ as cause and _b_ as effect. We say "at one and the same time," because the terms identifying and differentiating are correlatives which denote two different and opposing sides of one and the same ideational process viewed logically.
Accordingly, there is here on need of emphasizing that the act of relating, which enables us to think _a_ as cause and _b_ as effect, is an act of thought also, because it presupposes on our part an act of naming which raises it to being a component of our formulated and discursive thought. We therefore _think a_ as cause and _b_ as effect in that we apprehend the former as uniform _antecedens_ and the latter as uniform _consequens_.
[Footnote 10: Cf. the author"s "Umrisse zur Psychologie des Denkens," in _Philosophische Abhandlungen Chr. Sigwart ...
gewidmet_, Tubingen, 1900.]